Multifractals, Zeta functions, and spectra of complex dimensions

Orateur: LAPIDUS Michel
Localisation: Université de Californie, Riverside, États-Unis
Type: Séminaire cristolien d'analyse multifractale
Site: UPEC
Salle: Amphithéatre Vert
Date de début: 31/05/2012 - 16:15
Date de fin: 31/05/2012 - 16:15

As is well known multifractals are inhomogeneous measures (or functions) which are typically described by a full spectrum of real dimensions, as opposed to a single real dimension. Results from the study of fractal strings in the analysis of their geometry, spectra and dynamics via certain zeta functions and their poles (the complex dimensions) are used in this work as a springboard to define similar tools fit for the study of multifractals such as the binomial measure. The corresponding spectra (or ”tapestries”) of complex dimensions are indexed by the usual real multifractal spectrum. The goal of this talk is to shine light on new ideas and perspectives rather than to summarize a coherent theory. Progress has been made which connects these new perspectives to and expands upon classical results, leading to a healthy variety of natural and interesting questions for further investigation and elaboration.